1. CHAPTER 1 INTRODUCTION Squeeze casting, also known as liquid-metal forging, is a process by which molten metal solidifies under pressure within closed dies positioned between the plates of a hydraulic press [1,2]. The applied pressure and the instant contact of the molten metal with the die surface produce a rapid heat transfer condition that yields a pore-free fine-grain casting with mechanical properties approaching those of a wrought product. Due to the elimination of air gap between the metal and die interface, the heat transfer coefficient is increased, which enhances cooling rates and solidification. The squeeze casting is easily automated to produce near-net to net shape high- quality components. The process was introduced in the United States in 1960 and has since gained widespread acceptance within the non ferrous casting industry. Aluminium, Magnesium, Copper alloys components are readily manufactured using this process. Several ferrous components with relatively simple geometry for example, Nickel hard-crusher wheel inserts have also been manufactured by the squeeze casting process. Despite the shorter die life for complex life for complex ferrous castings requiring sharp corners within the die or punch, the process can be adopted for products where better properties and savings in labour or material costs are desired. 1.1 Background The process of mold design in the foundry industry has long been based on the intuition and experience of foundry engineers and designers. To bring the industry to a more scientific basis the design process should be integrated with scientific analysis such as fluid flow, heat transfer and stress analysis. Perhaps the most effective way to do this is with the aid of computer aided operation (CAO). Starting with the original design, a computer model is used to stimulate the casting process. Given a set of defect criteria, defects can be predicted modification to the original design. After several iterations of this design cycle and optimum design, free of defects should be produced. From this procedure it will be possible to determine whether a given mold design will produce a sound casting without having to discover this in the foundry through the usual trial and error process, which can be very tedious, time consuming and expensive.

2. Figure 1.1 Schematic Diagram of Casting Design Process Obviously the performance of this design cycle is based on the accuracy of the casting simulation and the validity of the defect prediction criteria. The promise of CAO has been that has we model the physical process closer to reality, the simulation process becomes more accurate, the defect criteria simpler and more precise. However, this promise comes at a price. First, as a model improves it becomes increasingly sensitive to the thermo physical data. Often this data is difficult to obtain. Therefore several new experimental techniques need to be developed. Second, as the mathematics becomes more complex there is a need to either develop efficient solution algorithm or invest in more powerful computer resources. It is a balance of all these factor that will result in a successful CAO application. The numerical simulation has increasingly become an effective tool in the casting manufacturing, by which some primitive and time-consuming procedures for finding the appropriate set of process parameters are avoided. The aim of this thesis is to improve the design cycle by investigating the heat transfer aspects of solidification during squeeze casting process. 1.2 Strategy of Thesis Design Casting Simulation Defect prediction Design modification 3. Recently Sun [3] has carried out extensive experiments on squeeze casting process of a different wall-thickness 5-step casting under different pressure conditions. Squeeze casting of magnesium alloy AM60 was performed under an applied pressure 30, 60 and 90 MPa in a hydraulic press. With measured temperatures, heat fluxes and IHTCs were evaluated using the polynomial curve fitting method and numerical inverse method. In this thesis, solidification process during squeeze casting process is simulated using the commercial CFD software FLOW-3D for the same set of parameters for which Sun [ ] has carried out experiments. The heat transfer coefficients needed for metal/mold inteface is taken from the polynomial fit developed by Sun [ ] which is explained in detail in chapter 4 of this thesis. The layout of the thesis is as follows: A literature review related to modeling and experimental studies related to squeeze casting process is presented in chapter 2. Chapter 3 explains the physics behind the squeeze casting process, corresponding governing equations and method of implementation using FLOW-3D,a commercial CFD software. Examination of existing mathematical models to determine their suitability. Chapter 4 explains in detail, the experimental setup used by Sun [3] to calculate heat transfer coefficients at the metal/die interface during squeeze casting process under different applied pressures. Construction and/ or importing of a mathematical model. Chapter 5 deals with the results and discussion part of the simulations doen using FLOW-3D. This is followed by conclusions in chapter 6. 1.3 Scope of Thesis The scope of this thesis has been restricted to the investigation of solidification process. In squeeze casting applied pressure plays an important role. The main advantage of the deployment of high pressure is that it enhances the heat transfer coefficients between liquid metal and mold surface by several orders of magnitude. This enhancement is realized due to the establishment of direct contact between the liquid metal and the die wall. This fact has been proved experimentally by Sun [3] where he has carried out extensive experiments to record temperature profiles during squeeze casting process of different wall- thickness 5-step casting under different pressure conditions. The alloy chosen for his experiments were magnesium alloy AM60 for the casting and steel die for the mold. From the experimental data, he back calculated the heat transfer coefficients at the metal/die interface using inverse approach and by polynomianl fitting method. This work is directed 4. towards using these heat transfer coefficients at the metal/die interface for simulating the solidification process of different wall-thickness 5-step casting under different pressure conditions and to map the temperature profiles at different locations and try to compare the results between simulation and experiments. CHAPTER 2 LITERATURE REVIEW 2.1 Squeeze Casting Casting is the most economical route to transfer raw materials into readily usable components. However, one of the major drawbacks for conventional or even more advanced casting techniques, e.g., high pressure die-casting is the formation of defects such as porosity. Furthermore, segregation defects of hot tears. New casting techniques have, therefore, been developed to compensate for these shortcomings. Of the many such casting techniques available, squeeze casting has greater potential to create less defective cast components. Squeeze casting (SC) is a generic term to specify a fabrication technique where solidification is promoted under high pressure within a re-usable die. It is a metal-forming process, which combines permanent mould casting with die forging into a single operation where molten metal is solidified under applied hydrostatic pressure. Although squeeze casting is now the accepted term for this forming operation, it has been variously referred to as "extrusion casting", "liquid pressing'', "pressure crystallization'' and "squeeze forming''. The idea was initially suggested by Chernov [2] in 1878 to apply steam pressure to molten metal while being solidified. However, in spite of its century old invention, commercialization of squeeze casting has been achieved only quite recently and is mainly concentrated in Europe and Japan. It is mainly used to fabricate high integrity engineering 5. components with or without reinforcement. Hartley [2] reported a technique developed by GKN Technology in UK for the pressurized solidification of Al alloy in reusable dies. In this process a die set is placed on a hydraulic press and preheated, and the exact amount of molten alloy is poured into the lower half of the open die set, the press closed so that the alloy fills the cavity and the pressure maintained until complete solidification occurs (31- 108MPa pressure). External undercut forms can be produced, and using retractable side cores, through-holes are possible. Since the as-fabricated components can be readily used in service or after a minor post-fabrication treatment, squeeze casting is also regarded as a net or near net-shape fabrication route. Parallel to commercialization, there are research centre throughout the world that are actively researching further development and exploitation of this net or near net shape fabrication process. This is evidenced by the publication of more than 700 papers in various engineering and scientific journals. These are mainly related to Aluminium and Magnesium- based alloys with special emphasis on metal matrix composites MMCs. According to Crouch[2], squeeze casting is now the most popular fabrication route for MMC artifacts. The annual 1215% growth rate of MMCs in the automotive, aerospace, sport and leisure goods and other markets is a clear indication of better usage of advanced manufacturing routes such as squeeze casting. In addition, since squeeze casting may be carried out without any feeding system, runners, gates, etc., and shrinkage compensating units, risers, the yield is quite high with almost no scrap for recycling. Finally, in contrast to forging, squeeze cast components are fabricated in a single action operation with lesser energy requirements. 2.1.1. Process outline The process of squeeze casting involves the following steps: 1. A pre-specified amount of molten metal is poured into a preheated die cavity, located on the bed of a hydraulic press. 2. The press is activated to close off the die cavity and to pressurize the liquid metal. This is carried out very quickly, rendering solidification of the molten metalunder pressure. 3. The pressure is held on till the metal is completely solidified. This not only increases the rate of heat flow, but also most importantly can eliminate macro/micro shrinkage porosity. 6. In addition, since nucleation of gas porosity is pressure-dependent, the porosityformation due to dissolved gases in the molten metal isrestricted. 4. Finally the punch is withdrawn and the component isejected out. 2.1.2.Mechanics of squeeze casting 2.1.2.1. The die A most crucial aspect in permanent mould castings such as die-casting or squeeze casting is the die itself and, most importantly, the design of the die including the selection of suitable die material, the manufacturing process, appropriate heat treatment and the maintenance practice. Squeeze casting dies are exposed to severe thermal and mechanical cyclic loading, which may cause thermal fatigue, cracking, erosion, corrosion, and indentation. The nature and features of die are greatly influenced by the particular alloy to be cast. Currently H13 tool steel is a widely used material of constructions but generally die steels should have good hot hardness, high temper resistance, adequate toughness and especially a high degree of cleanliness and uniform microstructure. 2.1.2.2. Different types of squeeze casting Two basic forms of the process may be distinguished, depending on whether the pressure is applied directly on to the solidifying cast product via an upper or male die (punch)or the applied pressure is exerted through an intermediate feeding system as schematically shown in Fig.2.1: (i) the direct squeeze casting mode, and (ii) the indirect squeeze casting mode. 7. Figure 2.1 Schematic diagram to illustrate the direct and indirect modes of the squeeze casting process. For the direct mode, two further forms may be distinguished based on liquid metal displacement initiated by the punch movement: (i) without metal movement, and(ii) with metal movement. As illustrated in Figure1.2, the first form is suitable for ingot type components where there is no metal movement, whilst the second type involving metal movement, also known as the backward process, is more versatile and can be used to cast a wide range of shaped components. Figure 2.2 Schematic diagram to show two forms of the direct squeeze casting process. 2.1.2.3. Various modes of squeeze casting Squeeze casting can be classified according to type of equipment used as : (i) vertical die closing and injection, (ii) horizontal die closing and injection, (iii) horizontal die closing and vertical injection, and (iv) vertical die closing and horizontal injection. A further classification may be envisaged as: (i) before the beginning of crystallization, and (ii) after the beginning of crystallization, which may also be described as semi-solid pressing. 8. Figure 2.3 summarizes the various modes of the squeeze casting process. Figure 2.3 Various modes of squeeze casting process 2.1.2.4 Process parameters The most important process parameter is the alloy itself. The composition and physical characteristics of the alloy are of paramount importance due to their direct effects on the die life. These include the melting temperature, and thermal conductivity of the alloy together with the combined effect of the heat-transfer coefficient and soldering onto the die material. Furthermore, the alloy dictates the selection of casting parameters such as die temperature, which has direct consequence on the die life. Therefore, squeeze casting is usually employed for low melting point temperature alloys of Aluminium and Magnesium. In addition to the composition of a casting alloy, which determines its freezing range and affects the quality of finished components, the casting parameters should also be controlled very closely to achieve a sound casting. The most dominant process parameters are die 9. temperature and pouring temperature, and superheat, although the level of applied pressure is also important. Since the metal is cast under pressure, the inherent castability of the alloy is of little or no concern. Other important parameters include the cleanliness of the metal in relation to the presence of inclusions, metal movement within the die which may induce turbulence, the die coat, and the time interval over which the pressure is applied, i.e., the so- called dead time. The die temperature is usually held at between 200C and 300C for Aluminium and Magnesium alloys, whilst the applied pressure varies between 50 and 150 MPa. The lubrication medium, i.e., the die coat, is usually graphite based. Heat-transfer coefficients are extremely high due to the casting metal being pressed against the die wall. The control of following process parameters is important for a good quality squeeze casting components.[19]. Melt Volume Precision control of the metal volume is required when filling the die cavity. This ensures dimensional control. Casting Temperature Depends on the alloy and part geometry. The starting point is normally 10-100C. above the liquidus temperatures. Tooling temperatures ranging from 200-300 C are normally used. The lower range is more suitable for thick section casting. The punch temperature is kept 15 - 30C below the lower die temperature to maintain sufficient clearance between them for adequate vending. Excess punch to die clearance allows molten metal to be extruded between them, eroding the surface. Time delay is the duration between the actual poring of the metal and the instant the punch contracts the molten pool and starts the pressurization of the thin webs that are incorporated into the die cavity. Because increased poring temperature maybe required to fill these sections adequately upon pouring, a time delay will allow for cooling of the molten pool before closing of the dies to avoid shrink porosity. Pressure levels of 50-140 MPa are normally used. There is an optimum pressure for each of the systems after this there is no added advantage in mechanical properties. Pressure duration varying from 30 - 120s has been found to be satisfactory for castings weighing 9kg. However, the pressure duration is again dependant on part geometry. Applied pressure after composite solidification and temperature equalization will not contribute any property enhancements and will only increase the cycle times. 10. Lubrication for Aluminium, Magnesium and Copper alloys a good grade of colloidal graphite spray lubricant has proved satisfactory when sprayed on the warm dies priority casting. Care should be taken to avoid excess build-up on narrow webs and fin areas where vent holes are used. Care must be taken to prevent plugging of these vents for ferrous casting, ceramic type coatings are required to prevent welding between the casting and the metal die surface. 2.1.3.Advantages of Squeeze Casting With the current emphasis on reducing materials consumption through virtually net shape processing and the demand for higher strength parts for weight savings, the emergence of Squeeze casting as a production process has given materials and process engineers a new alternative to the traditional approaches of casting and forging. By pressurizing liquid metals while they solidify, near-net shapes can be achieved in sound ,fully dense castings. The near-net and net shape capabilities of these manufacturing process are the key advantages of this process.Improved mechanical properties are additional advantages of Squeeze cast parts. The close contact with the die surface during solidification results in rapid solidification of casting. This rapid solidification produces a fine secondary dendrite arm spacing in the castings ,so that good strength and ductility can be attained. These excellent properties are relatively high in the as cast condition and are enhanced further in the heat treatable alloys by the excellent response to solution heat treatment. Since the process minimizes both gas porosity and shrinkage cavities, excellent properties are attained. These properties have been shown to be equivalent to wrought alloys in many instances. Although this process has many advantages in producing parts of light metals that can be utilized in structural applications ,the full potential can only be realized after the process has been optimized. Squeeze casting has been successfully applied to a variety of ferrous and non ferrous alloys in traditionally cast and wrought composition. Applications include aluminum alloy pistons for engines and disc brakes; automotive vehicles, truck hubs, barrel heads, and hubbed flanges; brass and bronzes bushings and gears; steel missile components and differential pinion gears; and a number of parts in cast iron, including ductile iron mortar shells [3]. Squeeze casting is simple and economical, and efficient in its use of raw material, and has excellent potential for automated operation at high rates of production. The process 11. generates the highest mechanical properties attainable in a cast product. The micro structural refinement and integrity of squeeze cast products are desirable for many critical applications. Squeeze casting process gives new opportunities to fabricate advanced materials, especially in the field of composites. Squeeze casting can also be used to fabricate bi-metals where, for instance, cast iron inserts can be incorporated to increase wear resistance in aluminum alloy components. Application to date have been wheels, pistons and brakes discs [19]. 2.1.4. Applications of Squeeze Casting Squeeze casting process has been explored for number of application using various metals and alloys. Due to low density and high strength-to-weight ratio, magnesium castings in the automotive application increase rapidly. Currently, high pressure die casting(HPDC) is the dominating production process for the most of magnesium automotive components. Compared with the HPDC, the squeeze casting process with high applied pressure is a promising solution for thick magnesium castings. The squeeze casting has been commercially succeeded in manufacturing parts include an Aluminium dome , ductile Iron mortar shell, and a Steel bevel gear. Other parts that have been Squeeze cast include stainless steel blades, super alloy discs, Aluminium automotive wheels and pistons, and gear blanks made of brass and bronze. Recently, this process has also been adopted to make composite material at an affordable cost. A porous ceramic pre-form is placed in the preheated die which is later filled with the liquid metal and pressure is then. The pressure, in this case, helps the liquid metal infiltrate the porous ceramic perform, giving a sound metal ceramic composite. The technological breakthrough of manufacturing metal-ceramic composites, along with the ability to make complex parts by a near-net shapes Squeeze casting process, suggest that this process will find application where cost considerations and physical properties of alloys are key factors [19].However, rare squeeze cast magnesium components have been used in real engineering applications. 2.1.5 Effect of pressure on the solidification behaviour during squeeze casting process 12. The application of pressure during solidification would be expected to affect phase relationships in an alloy system. This may be deduced by considering the Clausius-Clapeyron equation [2], f slff H VVT P T )( (2.1) where Tf is the equilibrium freezing temperature, Vl and Vs are the specific volumes of the liquid and solid, respectively, and Hf is the latent heat of fusion. Substituting the appropriate thermodynamic equation for volume, the effect of pressure on freezing point may roughly be estimated as follows [2]: )exp( f f O RT H PP (2.2) where P0, Hf and R are constants. Therefore, Tf should increase with increasing pressure. On a mechanistic approach, such change in freezing temperature is expected due to the reduction in interatomic distance with increasing pressure and thus restriction of atomic movement, which is the prerequisite for melting/freezing. The inter-solubility of constituent elements together with the solubility of impurity and trace elements is also expected to increase with pressure. Fig 2.4The effect of rapid cooling and the application of pressure on the Al-Si phase diagram. 13. The above mentioned theoretical predictions have been proven experimentally where a liquidus temperature rise of up to 90 C has been reported for pure Al/Si binary alloys at a pressure of 150 MPa. Furthermore, the eutectic point moves to the left, i.e., to higher Si contents as indicated in Figure 2.4. The consequences of such changes in the phase diagrams area significant improvement in the microstructure and mechanical properties of SC-fabricated components. The observed fine grained structure of squeeze castings being principally due to the increase in heat-transfer coefficients, i.e., greater cooling rates for the solidifying alloy due to reduction in the air gap between the alloy and the die wall and thus more effective contact area. The size of the air gap between the solidifying alloy and the die wall and the degree of undercooling, the two main features for fine structure, are dependent on such process parameters as the pressure, the timing of its application and the chemistry of the solidifying metal. Certainly, the application of pressure reduces the air gap between the solidifying metal and the metallic mould and thus increases the contact area; effecting improvement in the heat-transfer coefficient. Cho and Hong (1996) studied heat transfer coefficients at the casting/die interface in squeeze casting and applied a single load (50MPa) with die heating and concluded that heat transfer coefficient increases with the application of pressure. Casting parameters, as studied by different authors that have been known to have signicant inuence on the squeeze cast products are applied pressure, die pre-heat temperature and melt temperature. In the work of Maleki et al. (2006), squeeze casting products decrease in density at lower applied pressure and increases with higher applied pressures [14]. They concluded that this increase becomes less signicant at applied pressure of 100 MPa. In the report, it was also observed that with increase in applied pressure, the cast specimens grain size becomes smaller coupled with improved hardness. The melt temperatures of between 6900 C and 6600 C might just be enough for squeeze casting of Aluminium and Aluminium alloys respectively, as observed by Yang (2003) [15]. It was reported by Yang (2007) that the shorter the solidication time of casting, the higher is its density, yield strength and ultimate tensile strength [16]. Chattopadhyay (2007) applied a xed enthalpy formulation to model solidication for a cylindrical geometry and found that solidication time decreased asymptotically with increase in heat transfer coefcient [4]. This phenomenon, he sited was due to higher applied pressure on the solidifying cast product. Investigating varying parameters of squeeze casting process and its application, Ghomashchi and Vikhrov (2000) noted that many advances in squeeze casting of Aluminium and low melting metals are leading to the application of the process to high temperature alloys [2]. Santos et al. (2001) observed an increase in the heat transfer coefcients 14. with increasing melt superheat for horizontal directional solidication and a reverse for a vertical upward directional solidication [17]. 2.2 Definition of the problem Recently Sun [3] has carried out extensive experiments on squeeze casting process of a different wall-thickness 5-step casting under different pressure conditions. Squeeze casting of magnesium alloy AM60 was performed under an applied pressure 30, 60 and 90 MPa in a hydraulic press. With measured temperatures, heat fluxes and IHTCs were evaluated using the polynomial curve fitting method and numerical inverse method. In this thesis, solidification process during squeeze casting process is simulated using the commercial CFD software FLOW-3D for the same set of parameters for which Sun [ ] has carried out experiments. The heat transfer coefficients needed for metal/mold inteface is taken from the polynomial fit developed by Sun [ ] which is explained in detail in chapter 4 of this thesis. This work is directed towards using these heat transfer coefficients at the metal/die interface for simulating the solidification process of different wall-thickness 5-step casting under different pressure conditions and to map the temperature profiles at different locations and try to compare the results between simulation and experiments. The cast material chosen for this simulation is magnesium alloy AM60. The chemical composition of AM60 is shown in Table I. The thermal properties of the related materials in this study for performing the solidification simulation is shown in Table II . Based on Yu(2007)s work, the thermal conductivity(K) of AM60 has the linear relationship with its temperature and follows equations(K=192.8-0.187T) in semisolid temperature range(540C-615C) ; (K=0.0577T+60.85) below the solidus temperature(615C). 15. Table I Chemical composition of Magnesium Alloy AM60 Mg Al(%) Mn(%) Si(%) Cu()% Zn(%) balance 5.5-6.5 0.13 0.5 0.35 0.22 Table II Thermo physical properties of magnesium alloy AM60 Properties Mg Alloy AM60 Solid Liquid Thermal Conductivity (W/mK) 62 90 Specific Heat (J/Kg K) 1020 1180 Density (Kg/m3 ) 1790 1730 Latent Heat (KJ/Kg) 373 Liquidus Temp at 0Mpa(C) 615 Solidus Temp at 0Mpa(C) 540 16. CHAPTER 3 MATHEMATICAL MODELING OF CASTING PROCESS There are three forms of energy transport : conduction (diffusion transport), convection (heat transmitted by the mechanical motion of the fluid) and radiation (through space). All three are active during solidification of casting. Energy diffusion and convection occurs within the casting at the metal/mould interface and within the mould. Energy is transported by radiation from the mould to its environment which is typically the air. 3.1 Heat transfer Heat transfer is the single most important discipline in casting simulation. The solidification process depends on heat transfer from the part to the mould and from the mould to the environment. There are three possible modes of heat transfer (1) conduction (2) convection and the (3) radiation. The partial differential equation describing the process is given by Q z T k zy T k yx T k xt T cp (3.1) The solution of the above equation in a given domain requires knowledge of initial and boundary conditions. 3.1.1. Initial and Boundary Conditions The initial conditions define the temperature distribution throughout the domain at some initial point in time. The simplest option is to set the initial temperature depending on the estimated loss of superheat during mould filling. The initial mould temperature depends on the type of casting. Hence the mould temperature has to be fixed accordingly. For investment castings, the mould is preheated to a specified temperature which depend on the metal to be cast. Initial conditions (t=0) used for the simulation are: The pouring temperature of the molten alloy (MP of pure metal),Tmelt = 993K Temperature of the mould material , Tmould = 483K 17. The boundary condition describe the condition that must be satisfied on the boundaries of the domain. There are different types of boundaries viz., mold exterior walls, metal/mold ,metal/insulator, metal/chill, and metal/core interface and the metal free surfaces while simulating the casting process . Boundary condition used for the simulation: At the metal mold interface, the heat flux is governed by (3.2) Thermal conductivity of the cast metal - Thermal conductivity of the mold - interfacial heat transfer coefficient Hence the boundary condition to be specified at the metal mold interface is a heat transfer coefficient value 3.1.2 Mold exterior During the casting process, the molds exterior surface is in contact with air. Hence there exists a thermal boundary layer where the temperature varies from the surface temperature to the fluid free stream temperature. Either the temperature or heat flux can be prescribed as a boundary condition at this surface. But the most common approach is to approximate the heat flux at the solid surface (mold exterior) using Newtons law of cooling as am TThq (3.3) This is commonly referred to as the convective boundary condition. In equation (3.3) the terms Tm, Ta, q and h corresponds to the mold exterior temperature, ambient temperature, flux and convective heat transfer coefficient respectively. 3.1.3. Metal/mold or metal/chill or metal/insulator or metal/core interface moldcasti erface mold mold erface cast cast TTh n T K n T K intint 18. These boundaries are often referred to as interior boundaries. Generally there is a temperature discontinuity at these boundaries. For metal/mold interface the common approach is to express the interfacial heat flux as mcgap TThq (3.4) where Tc, Tm, hgap are the temperatures of the casting surface, mold surface and the gap heat transfer coefficient. Generally the gap heat transfer coefficient varies with respect to time or temperatures which are usually determined either by experiments or by an inverse heat transfer approach. 3.1.4. Metal free surfaces At the metal free surface, the cast metal is exposed to the ambient. The heat transfer at these surfaces can be modeled using a convective boundary condition as given by equation (3.3). 3.2 Solidification Solidification modeling involves the application of the heat transfer concept along with the technique to account for the release of latent heat during solidification[13]. The mold and any other solid materials like chill, insulators etc. are modeled using the standard heat conduction equation (equation 3.1). For the solidifying metal, a special procedure is required to accurately model the latent heat release. 3.2.1. Fraction of solid The extent of solidification at any location within the casting is represented by the fraction of solid, fs. At temperatures greater than or equal to the liquidus temperature, the cast metal is in a completely liquid state with a solid fraction value of zero. As the latent heat is removed, the fraction of solid increases and reaches a value of unity when the metal is in completely solid state. The temperature at this point is called the solidus temperature. The region where the solid fraction is between zero and unity is referred to as the mushy zone. There are several ways to describe the solid fraction variation between the liquidus and solidus temperatures. The simplest approach is to assume that the solid fraction varies linearly in the mushy zone. Alternatively, an analytical expression such as Scheils equation 19. may be used. The best approach is to determine the solid fraction-temperature relationship using experimental measurements. The more accurate method is using the solidification kinetics approach which involves the time integration of a solid fraction evolution equation. However solidification kinetics approach requires detailed metallurgical data which may not be known. 3.2.2 Latent Heat The release of latent heat during solidification is accounted for by a heat generation term t f HQ s f (3.5) where Hf represents the latent heat of solidification. This term is treated as a source term and is determined from known parameters which is explained as: The latent heat release rate is expressed as t T T f H t f H s f s f (3.6) This term can be included in the left hand side of equation (3.1) by defining an apparent specific heat as T f Hcc s fpapp (3.7) For the case where the solid fraction is assumed to vary linearly between liquidus and solidus, the above expression will be or lspapp ls s fpapp TTTTcc TTT T f Hcc (3.8) Hence the governing differential equation for solving solidification and heat transfer during casting process becomes 20. z T k zy T k yx T k xt T capp (3.9) with appropriate initial and boundary conditions. 3.3 Assumptions for the simulation (1) The die was assumed to be fully filled with liquid alloy at the start of simulation. This is a valid assumption when the cavity filling time is reasonably small so that the heat loss during filling time is negligible. (2) A uniform mold temperature was assumed for the simulation 21. 3.4 Flow 3D- An Overview FLOW-3D is a powerful and highly accurate commercial CFD software that gives engineers valuable insight into many of the physical processes. With special capabilities for accurately predicting free-surface flows, FLOW-3D is the ideal CFD software to use in design phase as well as in improving production processes [ ]. It employs specially developed numerical techniques to solve the equations of motion for fluids to obtain transient, three-dimensional solutions to multi- scale, multi-physics flow problems. An array of physical and numerical options allows users to apply the code to a wide variety of fluid flow and heat transfer phenomena. It is an easy-to-use simulation software designed to: Accurately simulate filling and solidification processes Pinpoint probable defects and problems before casting Identify viable designs more quickly Decrease the number of design iterations Improve scrap rates Reduce overall casting costs Flow-3D employs specially developed numerical techniques to solve the equations of motion for fluids to obtain transient, three-dimensional solutions to multi-scale, multi-physics flow problems. An array of physical and numerical options allows users to apply the code to a wide variety of fluid flow and heat transfer phenomena. Fluid motion is described with non-linear, transient, second-order differential equations. The fluid equations of motion must be employed to solve these equations. The science (and often art) of developing these methods is called computational fluid dynamics. A numerical solution of these equations involves approximating the various terms with algebraic expressions. The resulting equations are then solved to yield an approximate solution to the original problem. The process is called simulation. An outline of the numerical solution algorithms available in FLOW-3D follows the section on the equations of motion. Typically, a numerical model starts with a computational mesh, or grid. It consists of a 22. number of interconnected elements, or cells. These cells subdivide the physical space into small volumes with several nodes associated with each such volume. The nodes are used to store values of the unknowns, such as pressure, temperature and velocity. The mesh is effectively the numerical space that replaces the original physical one. It provides the means for defining the flow parameters at discrete locations, setting boundary conditions and, of course, for developing numerical approximations of the fluid motion equations. The FLOW-3D approach is to subdivide the flow domain into a grid of rectangular cells, sometimes called brick elements. A computational mesh effectively discretizes the physical space. Each fluid parameter is represented in a mesh by an array of values at discrete points. Since the actual physical parameters vary continuously in space, a mesh with a fine spacing between nodes provides a better representation to the reality than a coarser one. We arrive then at a fundamental property of a numerical approximation: any valid numerical approximation approaches the original equations as the grid spacing is reduced. If an approximation does not satisfy this condition, then it must be deemed incorrect. Reducing the grid spacing, or refining the mesh, for the same physical space results in more elements and nodes and, therefore, increases the size of the numerical model. But apart from the physical reality of fluid flow and heat transfer, there is also the reality of design cycles, computer hardware and deadlines, which combine in forcing the simulation engineers to choose a reasonable size of the mesh. Reaching a compromise between satisfying these constraints and obtaining accurate solutions by the user is a balancing act that is a no lesser art than the CFD model development itself. Rectangular grids are very easy to generate and store because of their regular, or structured, nature. Nonuniform grid spacing adds flexibility when meshing complex flow domains. The computational cells are numbered in a consecutive manner using three indices: i in the x- direction, j in the y-direction and k in the z direction. This way each cell in a three-dimensional mesh can be identified by a unique address (i, j, k), similar to coordinates of a point in the physical space. Structured rectangular grids carry additional benefits of the relative ease of the development of numerical methods, transparency of the latter with respect to their relationship to the original physical problem and, finally, accuracy and stability of the numerical solutions. The oldest numerical algorithms based on the finite difference and finite volume methods have been originally developed on such meshes. They form the core of the numerical approach in FLOW-3D. The finite difference method is based on the properties of the Taylor expansion and on the straightforward application of the definition of derivatives. It is the oldest of the methods applied to obtain numerical solutions to differential equations, and the first application is considered to have been developed by Euler in 1768. The finite volume method derives directly from the integral form of 23. the conservation laws for fluid motion and, therefore, naturally possesses the conservation properties. Rather than point wise approximations on a grid, FVM approximates the average integral value on a reference volume. FVM partitions the computational domain into control volumes (which are not necessarily the cells of the mesh).It then discretizes the integral formulation of the conservation laws over each control volume (making use of the Gaussdivergence theorem). It then solves the resulting set of algebraic equations or updates the values of the dependent variables. The key to the method is that the integral form of the conservation law can be rewritten; using the Gauss Divergence Theorem. In other words, the rate of change of mass in the control volume is equal to the net mass flux through its boundary. The domain of the current problem is divided into finite control volumes using cubic cells. 3.5Simulation strategy The steps involved in simulating the casting solidification process using FLOW3D are shown in the flowchart: Geometry modeling of the casting Identification of the material type of each component Activating physical models Applying Initial and Boundary Conditions Preprocessor Simulation Run Simulation Meshing the geometry 24. Figure 3.1 Flowchart for implementation of solidification simulation in FLOW-3D As a first step the solidification simulation of 5-step casting with the following dimensions for the steps: step 1 of dimensions 100 X 30 X 3 mm, step 2 of dimension 100 X 30 X 5 mm, step 2 of dimension 100 X 30 X 8 mm, step 4 of dimension 100 X 30 X 12 mm, step 2 of dimension 100 X 30 X 20 mm, is carried out using FLOW-3D. The whole casting geometry was created as a solid model in AutoCAD along with the bottom cylindrical shape sleeve of diameter 100 mm. This solid model was first converted to an .stl file . This file was used as the computational domain in the CFD software FLOW 3-D. The implementation of solidification simulation in FLOW -3D is briefly explained here: 3.5.1 Geometry modeling of the casting The first task is to create the computational domain for casting and mold. The mold box is created as a rectangular component using the primitive Box in FLOW-3D. Appropriate dimensions were chosen so that it covers the casting geometry in all directions. For the present simulation the dimensions of the mold box chosen was 160 X 140 X 270 mm. This is identified as component 1 and is a solid component. The 5-step casting geometry was then imported as an .stl file in FLOW-3D as a subcomponent to component 1 and this is identified as subcomponent 1. Since it is easier to work with SI units, appropriate transformations were done to convert the scale of the geometry from mm to m. Once the stl file is imported, the somponent type is transformed from solid to complement as shown in Figure 3.2. Analyzing Results 25. Figure 3.2 FLOW-3D GUI for creating computational domain 3.5.2 Identification of the material type The component1 is chosen as mold material and is made of steel and hence the material type loaded is Steel AISI P- 20 from the materials tab - solid database. The fluid 1 which corresponds to metal cavity (subcomponent 1 ) is chosen as the cast alloy and for the present simulation it was chosen as AM60 Magnesium alloy. The schematic view of the material database of FLOW-3D is shown in Figures 3.3 and 3.4 . Figure 3.3 FLOW-3D GUI for material selection - solids 26. Figure 3.4 FLOW-3D GUI for material selection - fluids 3.5.3 Meshing the geometry The first step in defining a particular domain is to determine the type of coordinate system to use for the mesh. Two types are available in FLOW-3D: Cartesian and cylindrical. The choice of mesh (cylindrical or Cartesian) does affect some of the geometry definitions. The selection of coordinate system applies to all mesh blocks. Cartesian meshes accommodate general geometries rather well and are therefore best for most problems. They are the default setting as indicated in the Mesh Type drop-down box. Cylindrical meshes can provide considerable improvements over Cartesian meshes for certain geometries that lend themselves to a cylindrical description, especially when the problem can be considered axisymmetric. Existing mesh block definitions may be modified in the tree structure. The resolution is controlled by the value specified for either the size of cell, or the total number of cells, or the number of the cells specified in each coordinate direction. When the geometry becomes complex shaped , intermediate mesh planes can be defined, as well as cell sizes for the domain between any two mesh planes. Figure 3.5(a) depicts the mesh domain in FLOW-3D and Figure 3.5(b) shows the mesh information for the computational domain. 27. Fig 3.5 (a) Meshed computational domain (b) mesh information dialog box For the present simulation, cell size chosen is 2 mm in each direction. Hence the total number of cells in the computational domain was around 245000 cells in the mesh. 3.5.4 Activating physical models The physical models were activated from physics tab where the gravity, heat transfer and solidification models were activated for the current simulation. In the gravity model the value of acceleration due to gravity was entered in the desired direction. For the present simulation a value of -9.8 m/s2 was given in the y -direction. In the heat transfer model the full energy equation option is chosen with implict numerical approximation Figure 3.6 shows the GUI of 28. FLOW-3D for implementation of physics. Fig 3.6 Dialog box of FLOW-3D where the physical models are activated. 3.5.5 Applying initial and boundary conditions For the present simulation it was assumed that the cavity was initially filled with liquid alloy. Hence the whole cavity which is considered as fluid domain was assigned the same initial temperature. The initial temperature of the fluid was specified as 993K using the initial conditions setting tab of FLOW-3D. The mold temperature was specified as 483 K using the initial conditions setting tab of FLOW-3Dfor mold material. All the external boundaries which corresponds to mold exterior was set to symmetry boundary condition. The interface between mold and metal is treated as a boundary and a typical value of heat transfer coefficient is specified . 29. 3.5.6 Numerics Tab The user can adjust parameters associated with the numerical methods used during a simulation in the Numerics Tab of FLOW-3D. There are six control options; (i) Time step controls - use the entry boxes in this group to change the initial time step size , minimum time step and the maximum time step. (ii) Pressure solver options - radio button to choose the desired pressure iteration scheme. (iii) Explicit / Implicit solver options - To change the numerical options associated with viscosity, heat transfer,elastic stress,surface tension,and the bubblepressure. Also the user can use the convergence controls buttons to modify the default convergence criteria if desired, when implicit options are selected. (iv) Volume of Fluid Advection - radio button option for choosing advection scheme for volume of fluid (v) Momentum Advection Group - radio button option for choosing the approximations for partial derivatives in momentum equations. (vi) Fluid Flow Options - radio button option through which the user can opt either for fluid flow or no fluid flow. The user has the option to choose either constant fluid velocity or zero fluid velocity for the fluid domain. Otherwise the full momemtum equations will be solved. Figure 3.7 shows the GUI corresponding to numeric option in FLOW-3D. 30. Figure 3.7 GUI for numerics in FLOW-3D 3.5.7 Output Tab The output tab of FLOW-3D is used for generating results for post processing. The user has the option to generate result files based on either time, or fill fraction or solidified fraction. The user also has the option to choose what data he needs to store in the results file like temperature, solid fraction, liquid fraction, wall temperature, wall heat flux etc. Also through probes GUI, the user can generate data corresponding to a particular location at all time intervals of the simulation. The GUI correponding to output tab of FLOw-3D is shown in Figure 3.8. 31. Figure 3.8 GUI for output tab in FLOW-3D 3.5.8 Simulation Manager The GUI corresponding to the Simulate tab of FLOW-3D is shown in Figure 3.9. Using this tab, the user can either start the "preprocess simulation" or "run simulation" option. If the user chooses "preprocess simulation", FLOW3D solver checks whether there are any errors associated with physics setting, meshing, property setting etc. If there are any errors , the solver comes out with error messages. If there are no errors, a file by name "flsgrf.*" is created and this file is the one which is used for running the solver. 32. Figure 3.9 GUI for output tab in FLOW-3D. Once the pre-processing is done the user can use the "run simulation" option to start the solver run. The "run simulation" option opens another window as shown in Figure 3.10 which shows the progress of the simulation and the data files available for post processing is also shown in this window. Figure 3.10 Simulation window of FLOW-3D. 33. One of the most valuable additions to the "Simulation Manager" tab is the introduction of a robust "Queue Manage tab" which is shown in Figure 3.11. The "Queue Manager" is especially useful for managing many simulations with changing priorities. For example, the "Queue Manager" allows simulations to be added to the queue, reordered, paused, restarted, and terminated. These actions are performed using the buttons located below the Queue Manager. Figure 3.11 Queue manager tab FLOW-3D. 3.5.9 Post-processing The post processing option in FLOW-3D is carried out using the "analyze tab" which is shown in Figure 3.12. Here the user has to load the simulation file for which post processing has to be done. The post processor of FLOW-3D can generate one dimensional, two dimensional and three dimensional contour plots, history plots like cooling curves at specified locations or spatial plots of temperature etc. If the user wants to generate text files of the data generated through simulation, he can do so by exporting the data as .txt file. Further movies can be generated for visualizing the mold filling, solidification profile etc. The post 34. processing window of FLOW-3D is shown in Figure 3.13. Figure 3.12 Analyse tab FLOW-3D. 35. Figure 3.12 GUI for choosing options for post processing in FLOW-3D. 36. CHAPTER 4 CASE STUDY EXPERIMENTAL RESULTS REPORTED BY SUN ET AL FOR ESTIMATION OF HEAT TRANSFER COEFFICIENT DURING SQUEEZE CASTING PROCESS 4.1 INTRODUCTION In this chapter, the experimental results of Sun et al [ ] is presented where they have done experiments to record the thermal histories at certain locations and how they back calculated the heat transfer coefficient between metal/die interface by using polynomial extrapolation method. 4.2 EXPERIMENTAL SETUP 4.2.1 5-Step Casting A 5-step shape casting was designed by Sun et al specifically to record the thermal histories at certain locations during squeeze casting process.. Figure 4.1 shows the 3-D model of 5- step casting used for their experimental study. It consists of 5 step casting, with dimensions of 100 x 30 x3 mm, 100 x 30 x 5 mm, 100 x 30 x 8 mm, 100 x 30 x12 mm, 100 x 30 x 20 mm accordingly. The molten metal was allowed to fill ths cavity from the bottom by a cylindrical shape sleeve with diameter 100 mm. Fig 4.1 3-D model of 5-step casting with the round-shape gating system [ Sun et al., [ ]] (a) XZ view; (b) YZ view; (c) isometric view 37. 2.2 Configuration of die and installation of measurement unit. To measure the temperatures and pressures at the casting-die interface accurately and effectively, a special thermocouple holder was developed. It hosted 3 thermocouples simultaneously to ensure accurate placement of thermocouples in desired locations of each step. The thermocouple holders were manufactured using the same material P20 as the die to ensure that the heat transfer process would not be distorted. Figure 4.2 illustrates schematically the configuration of the upper die (left and right parts) mounted on the top ceiling of the press machine. It also reveals the geometric installation of pressure transducers and thermocouple holders. Pressures within the die cavity were measured using Kistler pressure transducers 6175A2 with operating temperature 850C and pressures up to 200 MPa. As shown in Figure 4.2, pressure transducers and temperature thermocouples were located opposite to each other so that measurements from sensors could be directly correlated due to the symmetry of the step casting. Five pressure transducers and temperature measuring unit were designated as PT1 through PT5, TS1 through TS5, respectively. Each unit was inserted into the die and adjusted until the front wall of the sensor approached the cavity surface. The geometry shape of thermocouples holders was purposely designed the same as the pressure transducer, so that they could be exchangeable at different locations. Figure 4.2 Configuration of the upper die and the geometric installation of hermocouple and pressure transducers. (Sun et al., [ ]) 38. Figure 4.3 Installation of upper - die and geometric installation of thermocouples and pressure transducers. (Sun et al., [ ]) As shown in Figure 4.3, the thermocouple head was bent down to 90 degree and attached to the die surface tightly. The designed installation method minimized the disturbance of the temperature field in the step casting cavity. On the right part of the die, the thermocouples was installed to measure casting surface (T-surf) and inside die temperatures(T1,T2,T4). To ensure the accuracy, temperature measurements were also carried out simultaneously in both the right and the left parts of the die. This thermocouple head bending method enables to acquire relatively accurate data of the casting surface temperature. 4.2.2 Casting Process The integrated system included a 75 tons laboratory hydraulic press, upper-lower die, an that the mold assembly is composed of three parts. The two upper dies of the casting cavity is split along the center. The bottom sleeve has a diameter of 0.1016 m and a height of 0.127 m. The chill vent was located on the top of the step casting, which can discharge the gas inside the upper die cavity. Both the upper die and the bottom sleeve were heated by cartridge heaters. 39. Fig 4.4 Schematic diagram of squeeze casting machine used by Sun et al., [ ] Before pouring, the dies were pre-heated to 210C using four heating cartridges installed inside the dies. The experimental procedure included pouring molten magnesium alloy AM60 into the bottom sleeve with a pouring temperature 720C, closing the dies, cavity filling, squeezing solidification with the applied pressure, lowering the sleeve die, splitting the two parts of the upper die. Finally the 5-step casting can be shaken out from the cavity. The temperatures inside the die and casting were measured by Omega KTSS -116U thermocouples with response time below 10 ms. Real-time in-cavity local pressures and temperature data were recorded by a Lab VIEW based data acquisition system. The mold coating used in step castings is Boron Nitride lubrication (Type Sf) which was sprayed manually onto the surface of the mold cavity before heating the dies to the initial temperature. To minimize the thermal barrier effect of mold coating, the coating thickness applied in this study was relatively thin (below 50 m). 4.3. Determination Of IHTC by Polynomial Curve Fitting Method. To evaluate the IHTC effectively as a function of solidification time in the squeeze casting process, the finite difference method (FDM) was employed as follows based on the heat transfer equations. Since the thickness of each step is much smaller than the width or length of the step, it can be assumed that the heat transfer at each step is one-dimensional. The heat transfer across the nodal points of the step casting and die is shown in Figure 4.5. The temperatures were measured at 2, 4, 6, 8 mm beneath die surface and the heat flux transferred to the die mould can be evaluated by heat transfer equations. 40. Fig 4.5 One-dimensional heat transfer at the interface between the casting and die, where temperature measurements were performed (Sun et al. [ ]) Fig 4.6 5-step castings solidifying under applied pressure 30, 60, and 90MPa. (Sun et al., [ ] From the temperature versus time curves obtained at each position inside the die, the temperature at the die surface (X0 = 0mm) can be extrapolated by using polynomial curve fitting method. After the completion of filling, by selecting a particular time of solidification process, the values of temperatures were read from the temperature-time data at position X1, X2, X3, and X4 as shown in Figure 4.5. A polynomial curve with various measured temperatures against distance X were plotted and extrapolated by a polynomial trend line. The temperature at the die surface was determined by substituting the value of X=0 in the polynomial curve fitting. The polynomial equation thus obtained is 41. given below which predicts the temperature values at various distances inside the die at a chosen time. y = 0.0635x3 + 0.1759x2 - 16.495x + 308.43 This procedure is repeated for a number of time increments to get series of such temperatures with corresponding times at metal - die interface, at metal surface, die surface, and at various positions inside the die.